1. Math Tutoring Tips Learn The Basics
Shelley Todd, Southwestern Michigan College
Learn The Basics

2. Assisting Students to Overcome Common Math Errors
Discourage students from relying solely on memory.
Encourage them to see the underlying principles
This allows the student to correctly relate the new information to the old information that is already stored in their brains.
Below are some ways to guide the students you tutor in completing math problems.
Remind your students to read the problem directions
Remind your students to read the questions carefully to determine what exactly is being asked
Point out examples in the text that can be used to assist the student with step by step information on solving similar problems. Using this steps helps the student to know how to use the tools
Emphasize any rules that are needed to solve the problems
Suggest that students write down these rules on 3 by 5 cards and then use these cards when they are solving the problems
Emphasize the steps in the solving process – have your student write out each step as they work the problem

3. Student Holds the Pencil!
The tutor needs to let the student lead the tutorial session.
When the student holds the pencil, then he or she is directing the learning process.
If the tutor writes down the work then the student will passively agree.
When the student does the writing the tutor can see what the student really knows.
The key is to engage the learner with the material. Students learn best by doing. The tutor is there to provide direction and encouragement. The tutor should promote interaction and provide the student the time needed to process the material before expecting the student to respond.

4. Fundamental Errors Fundamental Errors in math are a big deal.
Don’t gloss over errors or mistakes
One “little” error can cause a big difference in the working of the problem and the answer.
Fundamental Errors provide the tutor with the opportunity to review the basics.
These teachable moments alert the student to what is important for them to learn and why.
An example of one of these fundamental error is the order of operations. If the order is not followed the problem will not work out correctly. Remember the Please excuse my dear aunt Sally. The P – stands for parenthesis, e stands for exponents, m stands for multiplication, d stands for division, a stands for addition, and S stands for subtraction. The other factor is to remind the students is that multiplication and division are of equal stature and which ever one comes first left to right must be completed first. The same is true of addition and subtraction.

5. Reinforce Caution
By learning to recognize dangerous math situations, a student can proceed carefully.
He or She will be well on the way to recognize that mathematics is not a collection of arbitrary disjointed facts.
Math is based on the fundamental principles.
Learning the fundamental principles are worth the time and effort.
For example if we use the fundamental principal of counting.
The fundamental principle of counting states:
If one task can be accomplished in x different ways
and, following this task, a second task can be
accomplished in y different ways, then the first task
followed by the second task can be accomplished in
x* y different ways.
Example 1 for a single event
A random number generator selects an integer from 1
to 40.
Find the number of ways a prime number is
selected.
Step 1 Analysis.
The prime numbers from 1 to 40 are:
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
therefore, there are 12 ways that this event can happen.
Emphasis is placed on connecting math to daily life and the work environment. When you have a student that says. I will never use math, or math is not necessary it is at this point that you as the tutor need to share how math is used daily and to help the student make the connection of how they effectively use math daily.
Do not try to learn math by memorizing formulas and examples. Most mathematics is based on a few fundamental principles and definitions. If you concentrate on these fundamentals and try to see how each new topic is simply another application, you will need to memorize very little new material.
Fun

6. Speak in Precise Terms When Tutoring – Speak Precisely Example:
When solving (x-2) (x-5) = 0. Do not say, “Set each term equal to 0”.
Say, “Since the product of these two terms is 0, at least one of them must be 0. Therefore, x - 2 = 0 or x – 5 = 0”
This makes direct use of the fundamental property of Zero.
Effective communication involves speaking to the students you tutor in a way they will understand. So that one does not confuse the student, the tutor should speak in the terms used in the textbook or the terms used by the student’s instructor.

7. Speak in Precise Terms
Repeat what the student says in more precise language.
Example: Student: “I will cancel out the one of the 6’s. Tutor: “That’s correct. Divide the numerator and denominator by 6.”
36 = 6 * 6 = 6 *
Tutor: “Can this problem be simplified further?”
Student:”Yes, 6 = 2 * 3 so the answer is 3 *
Effective communication between the tutor and student will help avoid confusion and frustration. Asking questions is a very good strategy to use to aid in effective communication.

8. Word Problems Can’t we just skip these? Please……….
Math strategy for word problems
SQRQCQ – Mnemonics Strategy for Effective Solving of word problems
The hardest part of word problems for students is to translate the word problem from the written word into a math equation. SQRQCQ provides students with a plan to complete word problems in a systematical method.
SQRQCQ:

9. SQRQCQ: S – Survey Q – Question R – Read - reread C – Compute
Word Problem:
Shelley has some porcelain tea cups. She was given 8 more for Christmas. Now she has 15. How many porcelain tea cups did she have before.
Survey – Carefully read the entire word problem to learn what it is about.
Clarify any terms you don’t understand.
Question – State the problem in the form of a question. The student comes up with a questions of what they believe the problem is asking for.
Read/Re-Read - Reading the problem out loud, visualizing it, or drawing a picture can help one state the problem as a question. This third step of reading/rereading helps the student to identify facts, discover the relevant information, and to pick out the details that are needed to solve the problem.
Question Now another question is formulated that should focus on what mathematical operation(s) to apply.
Compute – This is the step the student uses where they solve the problem
Question – There is where the student takes a look at the answer they discovered and looks at it and asks, “Is this answer correct?” “Does this answer make sense when I look back at the word problem.

10. SQRQCQ:
Survey – Carefully read the entire word problem to learn what it is about.
Clarify any terms you don’t understand.
This is what I know. Shelley has 8 tea cups and receives some more to make a total of 15 tea cups.
Question – State the problem in the form of a question.
Reading the problem out loud, visualizing it, or drawing a picture can help one state the problem as a question. Question – “How many tea cups did Shelley start out with?”
Using the SQRQCQ method the students should:
Survey the problem and notice that Shelley has 8 tea cups and receives some more to make a total of 15 tea cups.
Question – “How many items did Shelley start out with?”

11. SQRQCQ:
Read/Re-read – Identify the information that is needed to answer the problem.
Differentiate between information that is needed and information that is extra.
Write out the needed information as specific facts.
8 plus some number equals 15
Question – Ask, “What computations must I do to get the answer to the question?”
8 + S = 15 (students should realize that they have to subtract to find the answer because subtraction is the inverse operation of addition)
Reading/Re-reading would cause the student to think “8 plus some number equals 15”
Question - Then the student would question themselves: When I know a sum and one of the two addends, how can I find the other addend? So if 8 + Some number = 15, then how can I find some number. It is at this point that the students should realize that they have to subtract to find the answer, since subtraction is the inverse operation of addition.

12. SQRQCQ: Compute – Set up the problem on paper and do the computations.
8 + S = 15; 8 – 8 + S = ; so S = 7.
Check to make sure there are no errors in your work.
8 + S = 15; = 15
Question – Ask, “Does my answer make sense?”
Is the answer possible given the facts presented in the problem?
Check the relationship between the question and the answer.
Shelley started with 7 tea cups and received 8 more tea cups, would she have 15 tea cups? Yes, so the computation is correct so the problem was computed correctly.
Computing – is the next step and the student needs to work the problem. The equation could be set up as follows: 8 + S = 15; 8-8+S = 15-8; so S = 7.
The last step is to question themselves to see if the answer makes sense. Is it true that = 15? Shelley started with 7 tea cups and received 8 more tea cups, would she have 15 tea cups? Yes, so the computation is correct so the problem was computed correctly.

13. Why Review a Returned Test?
Tutor and student should review together the student’s past tests.
Know what questions were missed and why they were missed
Can work on those skills
Review the instructor’s comments so you can know what is expected.
Look at the type of questions that are used to help prepare for the next test.
Have the student rework all missed problems
Brainstorm strategies to use with different types of math problems.
Review how the student studied for the exam. Make suggestions for changes.
Why Review a Returned Tests? So that one doesn’t continue to make the same mistakes. Reviewing a past test is a excellent learning strategy. It lets one know what material is important, it reminds one of what has been learned, and it provides another way to review. After students take a test they generally want to move on. They think of the test as the end of the learning, but in actuality it is gage of where one is at and how much course material needs to be re-studied and re-worked. Math is a subject that builds one concept upon another. The material learned in the past chapter will still be needed in future chapters.

14. Questions for Reflection and Thought
What math tutoring strategies are you currently using?
Are they effective? (Why or Why not?)
What are your student’s main areas of concerns?
How can you apply this material in your tutoring sessions and in your tutoring center?

15. References
Hopper, C. (1998). Practicing College Study Skills. Houghton Mifflin.
Strichart, S. (N.D.). Teaching Study Strategies to Students with Learning Disabilities.